Bale had levelled at 2-2 with a header in the 25th minute, Ronaldo struck from the spot five minutes later after Baena had earned a second yellow card and conceded a penalty for a foul on Sergio Ramos and Bale sped clear and drove the ball low into the corner four minutes before the break.

With two men fewer, Rayo had little chance against waves of Real attacks and Benzema made it 5-2 three minutes into the second half before Ronaldo headed in a James Rodriguez cross in the 53rd.

The Portugal forward set up Bale for his hat-trick in the 61st and the Wales international completed his first four-goal haul with a 70th-minute tap-in to double his La Liga goals tally for the season to eight.

Benzema made it 9-2 in the 80th minute and Real hit double figures when the France international scored his third in the final minute.

It was the third time Real have scored 10 goals in a La Liga game and the first since they beat Elche 11-2 in 1960.

"We came out strongly but after we scored we relaxed," Real goalkeeper Keylor Navas said in an interview with Spanish television.

"Later we regained control and we managed to get a good result," added the Costa Rica international.

"It's normal that the fans are unhappy as we are not in first place which is where we are obliged to be and where we want to be."

Real have 33 points from 16 matches in third place, with champions Barca and Atletico each on 35 ahead of Atletico's match at Malaga later on Sunday.

Barca beat River Plate 3-0 to win the Club World Cup earlier on Sunday and will play their game in hand at Sporting Gijon in mid February.

Fourth-placed Celta Vigo can trim the gap to Real back to two points with a win at Granada later on Sunday, before Villarreal, a point behind Celta in fifth, play at Real Sociedad.